Solar Physics

, Volume 276, Issue 1–2, pp 395–406 | Cite as

The Amplitude of Sunspot Minimum as a Favorable Precursor for the Prediction of the Amplitude of the Next Solar Maximum and the Limit of the Waldmeier Effect

  • K. B. RameshEmail author
  • N. Bhagya Lakshmi


The linear relationship between the maximum amplitudes (R max) of sunspot cycles and preceding minima (R min) is one of the precursor methods used to predict the amplitude of the upcoming solar cycle. In the recent past this method has been subjected to severe criticism. In this communication we show that this simple method is reliable and can profitably be used for prediction purposes. With the 13-month smoothed R min of 1.8 at the beginning, it is predicted that the R max of the ongoing cycle will be around 85±17, suggesting that Cycle 24 may be of moderate strength. Based on a second-order polynomial dependence between the rise time (T R) and R max, it is predicted that Cycle 24 will reach its smoothed maximum amplitude during the third quarter of the year 2013. An important finding of this paper is that the rise time cycle amplitude relation reaches a minimum at about 3 to 3.5 years, corresponding to a cycle amplitude of about 160. The Waldmeier effect breaks down at this point and T R increases further with increasing R max. This feature, we believe, may put a constraint on the flux transport dynamo models and lead to more accurate physical principles-based predictions.


Sunspot Solar cycle 24 Prediction Waldmeier effect 


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  1. Ahluwalia, H.S.: 2000, Solar cycle 23 prediction update. Adv. Space Res. 26, 187 – 192. MathSciNetADSCrossRefGoogle Scholar
  2. Ahluwalia, H.S., Ygbuhay, R.C.: 2010, Current forecast for sunspot cycle 24 parameters. In: AIP conf. Proc. 12th Solar Wind Conf., 671 – 674. doi: 10.1063/1.3395956. Google Scholar
  3. Brajša, R., Wöhl, H., Hanslmeier, A., Verbanac, G., Ruždjak, D., Cliver, E., Svalgaard, L., Roth, M.: 2009, On solar cycle predictions and reconstructions. Astron. Astrophys. 496, 855 – 861. ADSCrossRefGoogle Scholar
  4. Brown, G.M.: 1976, What determines sunspot maximum. Mon. Not. Roy. Astron. Soc. 174, 185 – 189. ADSGoogle Scholar
  5. Cameron, R., Schüssler, M.: 2008, A robust correlation between growth rate and amplitude of solar cycles: consequences for prediction methods. Astrophys. J. 685, 1291 – 1296. ADSCrossRefGoogle Scholar
  6. Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Predicting solar cycle 24 with a solar dynamo model. Phys. Rev. Lett. 98, 131103. ADSCrossRefGoogle Scholar
  7. Dikpati, M., Gilman, P.A.: 2006, Simulating and predicting solar cycles using a flux-transport dynamo. Astrophys. J. 649, 498 – 514. ADSCrossRefGoogle Scholar
  8. Dikpati, M., Gilman, P.A., de Toma, G.: 2008, The Waldmeier effect: an artifact of the definition of Wolf sunspot number? Astrophys. J. 673, 99 – 101. ADSCrossRefGoogle Scholar
  9. Du, Z.: 2011, The relationship between prediction accuracy and correlation coefficient. Solar Phys. 270, 407 – 416. ADSCrossRefGoogle Scholar
  10. Du, Z.L., Wang, H.N.: 2010, Does a low solar cycle minimum hint at a weak upcoming cycle? Res. Astron. Astrophys. 10, 950 – 955. CrossRefADSGoogle Scholar
  11. Du, Z., Wang, H., Zhang, L.: 2009a, Correlation function analysis between sunspot cycle amplitudes and rise times. Solar Phys. 255, 179 – 185. ADSCrossRefGoogle Scholar
  12. Du, Z.L., Li, R., Wang, H.N.: 2009b, The predictive power of Ohl’s precursor method. Astron. J. 138, 1998 – 2001. ADSCrossRefGoogle Scholar
  13. Harvey, K.L., White, O.R.: 1999, What is solar cycle minimum? J. Geophys. Res. 104, 19759 – 19764. ADSCrossRefGoogle Scholar
  14. Hathaway, D.H.: 2010, The solar cycle. Living Rev. Solar Phys. 7, 1 – 65. ADSGoogle Scholar
  15. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 1994, The shape of the sunspot cycle. Solar Phys. 151, 177 – 190. ADSCrossRefGoogle Scholar
  16. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 2002, Group sunspot numbers: sunspot cycle characteristics. Solar Phys. 211, 357 – 370. ADSCrossRefGoogle Scholar
  17. Javaraiah, J.: 2007, North-south asymmetry in solar activity: predicting the amplitude of the next solar cycle. Mon. Not. Roy. Astron. Soc. 377, 34 – 38. ADSCrossRefGoogle Scholar
  18. Kakad, B.: 2011, A new method for prediction of peak sunspot number and ascent time of the solar cycle. Solar Phys. 270, 393 – 406. ADSCrossRefGoogle Scholar
  19. Kane, R.P.: 1997, A preliminary estimate of the size of the coming solar cycle 23, based on Ohl’s precursor method. Geophys. Res. Lett. 24, 1899 – 1902. ADSCrossRefGoogle Scholar
  20. Karak, B.B., Choudhuri, A.R.: 2010, The Waldmeier effect in sunspot cycles. In: Hasan, S.S., Rutten, R.J. (eds.) Magnetic Coupling Between the Interior and Atmosphere of the Sun, 402 – 404. doi: 10.1007/978-3-642-02859-5-40. CrossRefGoogle Scholar
  21. Karak, B.B., Choudhuri, A.R.: 2011, The Waldmeier effect and the flux transport solar dynamo. Mon. Not. Roy. Astron. Soc. 410, 1503 – 1512. ADSGoogle Scholar
  22. Kennedy, J.B., Neville, A.M.: 1964, Basic Statistical Methods for Engineers and Scientists, Dun-Donnelley, New York, 180. Google Scholar
  23. Lantos, P.: 2000, Prediction of the maximum amplitude of solar cycles using the ascending inflexion point. Solar Phys. 196, 221 – 225. ADSCrossRefGoogle Scholar
  24. McKinnon, J.A.: 1987, Sunspot numbers, 1610 – 1985: based on “The sunspot activity in the years 1610 – 1960, by Prof. M. Waldmeier”, Report UAG, 0579-7144; 95. World Data Center A for Solar-Terrestrial Physics, Boulder, Colorado. Google Scholar
  25. Pesnell, W.D.: 2008, Predictions of solar cycle 24. Solar Phys. 252, 209 – 220. ADSCrossRefGoogle Scholar
  26. Petrovay, K.: 2010, Solar cycle prediction. Living Rev. Solar Phys. 1, 6 – 59. ADSGoogle Scholar
  27. Ramesh, K.B.: 2000, Dependence of SSNM on SSNm – a reconsideration for predicting the amplitude of a sunspot cycle. Solar Phys. 197, 421 – 424. ADSCrossRefGoogle Scholar
  28. Schatten, K.: 2005, Fair space weather for solar cycle 24. Geophys. Res. Lett. 32, 21106. doi: 10.1029/2005GL024363. ADSCrossRefGoogle Scholar
  29. Schatten, K.H., Scherrer, P.H., Svalgaard, L., Wilcox, J.M.: 1978, Using dynamo theory to predict the sunspot number during solar cycle 21. Geophys. Res. Lett. 5, 411 – 414. ADSCrossRefGoogle Scholar
  30. Solanki, S.K., Krivova, N.A., Schüssler, M., Fligge, M.: 2002, Search for a relationship between solar cycle amplitude and length. Astron. Astrophys. 396, 1029 – 1035. ADSCrossRefGoogle Scholar
  31. Svalgaard, L., Cliver, E.W., Kamide, Y.: 2005, Sunspot cycle 24: smallest cycle in 100 years? Geophys. Res. Lett. 32, 01104. doi: 10.1029/2005GL021664. CrossRefGoogle Scholar
  32. Waldmeier, M.: 1935, Neue Eigenschaften der Sonnenfleckenkurve. Astron. Mitt. 14, 105 – 130. ADSGoogle Scholar
  33. Wang, Y.M., Sheeley, N.R.J.: 2009, Understanding the geomagnetic precursor of the solar cycle. Astrophys. J. 694, 11 – 15. ADSCrossRefGoogle Scholar
  34. Wilson, R.M., Hathaway, D.H., Reichmann, E.J.: 1998, An estimate for the size of cycle 23 based on near minimum conditions. J. Geophys. Res. 103, 6595 – 6603. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Indian Institute of AstrophysicsKoramangalaIndia
  2. 2.Jyoti Nivas Pre-University & Degree CollegeKoramangalaIndia

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